The spin-mixing dynamics of large-spin fermions were experimentally realized recently,where a long-lived collective particle number oscillation between different spin states was observed[1,2].In this paper,we develop a time-dependent Hartree-Fock theory[3]to describe these spinor Fermi gases in a harmonic trap.We will study the effect of quadratic magnetic field and show how the collective oscillation originates from the two-body physics.Specifically,we consider the rotation angle dependence of the dynamics,similar like the experiment condition.Our calculation shows a oscillation period peak in the running phase regime,which is the remnant of the transition from resonant regime to Zeeman regime.We note this peak only appears for small rotation angle,which may be observed in future experiments.